A Theory of the Longitudinal and Hall Conductivities of the Cuprate Superconductors

TL;DR

This paper develops a theoretical framework based on a nearly antiferromagnetic Fermi liquid model to explain the temperature-dependent resistivity and Hall conductivity in cuprate superconductors, aligning well with experimental data.

Contribution

It introduces a perturbative and numerical approach to model transport phenomena in cuprates, incorporating magnetic crossovers and anisotropic quasiparticle lifetimes, advancing understanding of their normal state properties.

Findings

Quantitative agreement with experimental resistivity and Hall conductivity data.

Identification of hot and cold quasiparticle regions consistent with theory.

Demonstration of CuO chain effects on in-plane anisotropy.

Abstract

We establish the applicability to transport phenomena in the cuprate superconductors of a nearly antiferromagnetic Fermi liquid (NAFL) description of the magnetic interaction between planar quasiparticles by using it to obtain the temperature dependent resistivity and Hall conductivity seen experimentally in the normal state. Following a perturbative calculation of the anisotropic (as one goes around the Fermi surface) quasiparticle lifetimes which are the hallmark of a NAFL, we obtain simple approximate expressions for the longitudinal, $\sigma_{xx}$, and Hall, $\sigma_{xy}$, conductivities which reflect the magnetic crossovers seen experimentally as one varies the doping level and temperature. We present a simple phenomenological model for the variation in mean free path around the Fermi surface, and use this to extract from experiments on $\sigma_{xx}$ and $\sigma_{xy}$ quasiparticle lifetimes in the hot (strongly coupled quasiparticle) and cold (weakly coupled quasiparticle) regions of the Fermi surface which are consistent with the perturbation theory estimates. We improve upon the latter by carrying out direct numerical (non-variational) solutions of the Boltzmann equation for representative members of the YBa$_2$Cu$_3$O$_{6+x}$ and La$_{2-x}$Sr$_x$CuO$_4$ systems, with results for transport properties in quantitative agreement with experiment. Using the same numerical approach we study the influence of CuO chains on the a-b plane anisotropy and find results in agreement with experimental findings in YBa$_2$Cu$_4$O$_8$.